Related papers: A central limit theorem for a sequence of conditio…
The Central Limit Theorem provides a foundation for inferential statistics and hypothesis testing. It describes how standardized statistics behave under repeated sampling from large populations. However, if the size of the sample (n)…
We study dynamical systems arising as time-dependent compositions of Pomeau-Manneville-type intermittent maps. We establish central limit theorems for appropriately scaled and centered Birkhoff-like partial sums, with estimates on the rate…
We prove a central limit theorem for non-commutative random variables in a von Neumann algebra with a tracial state: Any non-commutative polynomial of averages of i.i.d. samples converges to a classical limit. The proof is based on a…
In this paper, we derive a central limit theorem for collections of weakly correlated random variables indexed by discrete metric spaces, where the correlation decays in the distance of the indices. The correlation structure we study…
Over the last 30 years, extensive work has been devoted to developing central limit theory for partial sums of subordinated long memory linear time series. A much less studied problem, motivated by questions that are ubiquitous in extreme…
Let I_1,...,I_n be independent but not necessarily identically distributed Bernoulli random variables, and let X_n=\sum_{j=1}^nI_j. For \nu in a bounded region, a local central limit theorem expansion of P(X_n=EX_n+\nu) is developed to any…
We establish central limit theorems for the position and velocity of the charged particle in the mechanical particle model introduced in the paper "Limit velocity for a driven particle in a random medium with mass aggregation"…
We provide rates of convergence in the central limit theorem in terms of projective criteria for adapted stationary sequences of centered random variables taking values in Banach spaces, with finite moment of order $p \in ]2,3]$ as soon as…
We prove results about uniform convergence of densities in the free central limit theorem without assumptions of boundedness on the support.
The purpose of this paper is to study the limiting distribution of special {\it additive functionals} on random planar maps, namely the number of occurrences of a given {\it pattern}. The main result is a central limit theorem for these…
The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in presence of strong correlations between the added random contributions. Here, we study this problem for…
In this talk I first review at an elementary level a selection of central limit theorems, including some lesser known cases, for sums and maxima of uncorrelated and correlated random variables. I recall why several of them appear in…
We consider the asymptotic normalcy of families of random variables $X$ which count the number of occupied sites in some large set. We write $Prob(X=m)=p_mz_0^m/P(z_0)$, where $P(z)$ is the generating function $P(z)=\sum_{j=0}^{N}p_jz^j$…
In this paper, we provide a central limit theorem for the finite-dimensional marginal distributions of empirical processes $(Z_n(f))_{f\in\mathcal{F}}$ whose index set $\mathcal{F}$ is a family of cluster functionals valued on blocks of…
We consider sequences of random variables whose probability generating functions are polynomials all of whose roots lie on the unit circle. The distribution of such random variables has only been sporadically studied in the literature. We…
We consider a non-nestling random walk in a product random environment. We assume an exponential moment for the step of the walk, uniformly in the environment. We prove an invariance principle (functional central limit theorem) under almost…
The typical central limit theorems in high-frequency asymptotics for semimartingales are results on stable convergence to a mixed normal limit with an unknown conditional variance. Estimating this conditional variance usually is a hard…
We consider a simple random walk (dimension one, nearest neighbour jumps) in a quenched random environment. The goal of this work is to provide sufficient conditions, stated in terms of properties of the environment, under which the Central…
The study of the normalized sum of random variables and its asymptotic behaviour has been and continues to be a central chapter in probability and statistical mechanics. When those variables are independent the central limit theorem ensures…
The Central Limit Theorem for Iterated Functions Systems on the circle is proved. We study also ergodicity of such systems.